<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml7" display="inline" overflow="scroll" altimg="si3.gif"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> control of Markov jump time-delay systems under asynchronous controller and quantizer

This paper aims to design an asynchronous state feedback controller for Markov jump time-delay systems. The highlight of this work lies in that the state feedback is quantized by a logarithmic quantizer, and both the controller and quantizer are asynchronous with the controlled systems. By Lyapunov–Krasovskii functional, a sufficient condition is presented to ensure that the resulting closed-loop system is stochastically mean square stable with a prescribed H ∞ performance index. Finally, an example is presented to illustrate the effectiveness and new features of proposed design method.